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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 423 · 40 sums
TalentJR

The method (Letters one side, numbers the other): Open brackets: a(x − b) = ax − ab. Fractions: multiply both sides by the LCM of the denominators — x/3 + x/4 = 14 → 4x + 3x = 168. Move letter terms to one side and numbers to the other (change the sign when a term crosses =), then divide. Word problems: consecutive numbers are n, n + 1, n + 2 …; ages in y years are age + y.

NameDateTime takenScore ___ / 40
  1. 1.Solve: 4(x − 1) = x + 5. What is x?
  2. 2.The length of a rectangle is 4 cm more than its width. Its perimeter is 92 cm. What is its width (in cm)?
  3. 3.Solve: 3p + 4 = 2p + 16. What is p?
  4. 4.Solve: 6(p − 3) = 4p + 22. What is p?
  5. 5.Solve: m/3 + m/4 = 14. What is m?
  6. 6.The sum of four consecutive whole numbers is 202. What is the largest of them?
  7. 7.Solve: 4m + 20 = 2m + 36. What is m?
  8. 8.A father is 14 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  9. 9.The sum of two consecutive whole numbers is 95. What is the smallest of them?
  10. 10.Solve: 9y + 15 = 4y + 30. What is y?
  11. 11.Solve: 5(t − 5) = 3t + 3. What is t?
  12. 12.The length of a rectangle is 6 cm more than its width. Its perimeter is 84 cm. What is its width (in cm)?
  13. 13.Solve: 5y + 19 = y + 71. What is y?
  14. 14.The sum of four consecutive whole numbers is 118. What is the smallest of them?
  15. 15.Solve: 8n + 8 = 2n + 38. What is n?
  16. 16.A father is 12 years older than his son. In 2 years, the father will be three times as old as his son. How old is the son now?
  17. 17.A father is 21 years older than his son. In 4 years, the father will be four times as old as his son. How old is the son now?
  18. 18.A father is 27 years older than his son. In 2 years, the father will be four times as old as his son. How old is the son now?
  19. 19.Solve: 4(y − 1) = 3y + 1. What is y?
  20. 20.The length of a rectangle is 11 cm more than its width. Its perimeter is 74 cm. What is its width (in cm)?
  21. 21.Solve: 4y + 6 = y + 39. What is y?
  22. 22.Solve: y/4 + y/2 = 18. What is y?
  23. 23.Solve: 4(p − 5) = 2p + 10. What is p?
  24. 24.Solve: 7t + 6 = 3t + 18. What is t?
  25. 25.Solve: x/4 + x/3 = 35. What is x?
  26. 26.Solve: 3x + 3 = 2x + 10. What is x?
  27. 27.Solve: 6(x − 5) = 5x + 1. What is x?
  28. 28.The length of a rectangle is 11 cm more than its width. Its perimeter is 122 cm. What is its width (in cm)?
  29. 29.Solve: 5(y − 2) = 2y + 23. What is y?
  30. 30.A father is 38 years older than his son. In 7 years, the father will be three times as old as his son. How old is the son now?
  31. 31.Solve: t/6 + t/5 = 44. What is t?
  32. 32.The length of a rectangle is 4 cm more than its width. Its perimeter is 40 cm. What is its width (in cm)?
  33. 33.Solve: 4(t − 2) = 3t + 2. What is t?
  34. 34.A father is 15 years older than his son. In 3 years, the father will be four times as old as his son. How old is the son now?
  35. 35.The sum of two consecutive whole numbers is 105. What is the smallest of them?
  36. 36.Solve: 3(p − 4) = 2p + 12. What is p?
  37. 37.Solve: n/2 + n/6 = 8. What is n?
  38. 38.Solve: y/4 + y/3 = 21. What is y?
  39. 39.Solve: 3(p − 1) = p + 17. What is p?
  40. 40.The sum of two consecutive whole numbers is 83. What is the largest of them?

Answer key

  1. 3
  2. 21
  3. 12
  4. 20
  5. 24
  6. 52
  7. 8
  8. 6
  9. 47
  10. 3
  11. 14
  12. 18
  13. 13
  14. 28
  15. 5
  16. 4
  17. 3
  18. 7
  19. 5
  20. 13
  21. 11
  22. 24
  23. 15
  24. 3
  25. 60
  26. 7
  27. 31
  28. 25
  29. 11
  30. 12
  31. 120
  32. 8
  33. 10
  34. 2
  35. 52
  36. 24
  37. 12
  38. 36
  39. 10
  40. 42

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